1. Field of the Invention
The present invention concerns a method to correct image distortions that can occur upon acquisition of diffusion-weighted magnetic resonance (MR) images of an examination subject, as well as a magnetic (MR) resonance system with which such a method can be implemented.
2. Description of the Prior Art
In diffusion imaging, multiple images are normally acquired with different diffusion directions and weightings, and are combined with one another. The strength of the diffusion weighting is usually defined by what is known as the “b-value”. The diffusion images with different diffusion directions and weightings, or the images combined therefrom can then be used for diagnostic purposes. Parameter maps with particular diagnostic significance, for example, maps that reflect the “Apparent Diffusion Coefficient (ADC)” or the “Fractional Anisotropy (FA)”, can be generated by suitable combinations of the acquired, diffusion-weighted images.
Eddy current fields can disadvantageously be caused by the diffusion gradients, these eddy current fields in turn leading to image distortions having an appearance that depends both on the amplitude of the gradients (i.e. the diffusion weighting) and on their direction. If the acquired individual images are then combined with one another with no correction in order to generate (for example) the cited parameter maps, the distortions, which are different for every image, lead to incorrect associations of pixel information and therefore to errors (or at to a reduced precision) of the calculated parameters. Particularly in diffusion-weighted images that were acquired with the use of the echoplanar technique (EPI), eddy current-dependent distortions represent a particularly significant challenge, since a particularly high sensitivity (approximately 10 Hz per pixel in the phase coding direction) to static and dynamic field interference typically exists in EPI imaging, and high gradient amplitudes are specifically used here to adjust the diffusion gradients.
Multiple image-based methods to correct eddy current-dependent distortions in diffusion imaging are known. For example, in a publication by Haselgrove et al. (in MRM 36: 960-964, 1996) a method is described in which an undistorted MR reference image is initially acquired with b=0 (i.e. without application of a diffusion gradient). Furthermore, a second adjustment measurement with slight diffusion weighting is acquired for the direction to be corrected. For example, a slight diffusion weighting thereby means a b-value of 160 s/m2. It is then assumed that the distortions in the images can be described in good approximation as simple affine transformations with a scaling N, a shear S and a shift or, respectively, translation T. Distortion parameters for M, S and T are therefore determined with the aid of the two adjustment measurements, i.e. the measurement of the reference image and the image with low diffusion weighting. Using an extrapolation relationship, the distortion parameters M, S and T that are determined in this way are then utilized for the correction of the actual diffusion-weighted usable MR images in which the b-value amounts to 1000 s/m2, for example. This method requires at least one adjustment measurement for each diffusion direction.
Furthermore, in a publication by Bodammer et al. (in MRM 51: 188-193, 2004) a method is described in which two images with identical diffusion direction and diffusion weighting but inverted polarity are acquired within the framework of adjustment measurements. While the diffusion contrast remains unchanged given an inverted polarity, the inversion affects the distortion as an inversion thereof. This means that an extension becomes a compression, a positive shear becomes a negative shear and a positive translation becomes a negative translation. In this method two images must be respectively acquired for every diffusion direction and for every diffusion weighting.
In an article by Zhuang et al. entitled “Correction of Eddy-Current Distortions in Diffusion Tensor Images Using the Known Directions and Strengths of Diffusion Gradients,” J. Mag. Res. Imaging, Vol. 24, (2006) pp. 1188-1193, a type of adjustment method is described in which the geometric distortion properties of reference gradient pulses are measured once and then transferred to arbitrary gradient pulses according to a model.
It is common to all of the methods explained above that only the affine transformations (translation, scaling, shear)—i.e. image distortions of zeroth and first order—are taken into account in the correction. This occurs with the assumption that the dominant residual dynamic interference fields exhibit the same geometry in their spatial distribution as the causes of the interference (i.e. the diffusion gradients). However, in modern MR systems this assumption is not always correct. For example, the homologous interference fields may be compensated by a pre-distortion of the gradient pulse shape (known as the “pre-emphasis”) to the extent that the residual interference fields exhibit more complex geometries. For a precise combination of the diffusion-weighted images it is thus necessary to correct image distortions that go beyond affine transformations.
In US 2007/0223832 A1 different methods are described in order to achieve a correction of the diffusion-weighted images using mutual reference between two or more diffusion-weighted images. In most of the exemplary embodiments described there, it is likewise only linear transformations that are considered. Only in a last exemplary embodiment are more complex functions used, wherein it is proposed to use a function in an entirely general form with a cubic dependency on a column index while incorporating all expansion coefficients.
In a document by Rohde et al. (in MRM 51: 103-114, 2004) a simultaneous correction of the diffusion-weighted images is described both with regard to eddy current-dependent distortions and with regard to patient movements. For the correction the distorted coordinates of the diffusion-weighted measurement are mapped to target coordinates by means of a transformation. The transformation thereby consists of a movement portion and an eddy current portion. For the geometric transformations with regard to the eddy current portion, all field geometries up to and including those of the second order that satisfy the Laplace equation are considered. This method thus goes beyond the correction of purely affine transformations. In order to achieve an even better correction, however, it would be desirable to also take into account field geometries of much higher order.
It is a problem that the correction method takes longer the more complex the geometry that is to be taken into account in the distortion correction, since the computational effort for correction rises dramatically with the increasing number of parameters to be taken into account. The use of all possible field geometries up to the 2nd order as occurs in the method by Rohde et al., already leads to a relatively high computational cost.